Correlated spreading sequenes for high rate non-coherent communication systems

ABSTRACT

The invention relates notably to a method for modulating information symbols to be transmitted in a CDMA communication network by using a non-orthogonal modulation code comprising M spreading sequences (s m  1≦m≦M), each comprising in N chips (s m,n  1≦n≦N), the M spreading sequences having the same energy.  
     According to the invention, the amplitude of the chips take a plurality of values the number M of spreading sequences is higher than the number of chips N per spreading sequence.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to communication systems and inparticular to modulation of information symbols in communicationsystems.

[0002] In usual communication systems, for example wirelesscommunication systems, information symbols are coded and modulated atthe sender, transmitted on the medium and demodulated and decoded at thereceiver.

[0003] Depending on the communication system, demodulation can beperformed in a coherent or a non-cohere rent manner.

[0004] Coherent detection requires equalization and channel responseestimation so that the effects of phase and magnitude distortion causedby the communication channel can be compensated for with matchedfilters. Coherent demodulation brings prohibitive complexity and poorrobustness.

[0005] Non-coherent detection, on the contrary, is based on the factthat decision for received symbols can be made without compensating forthe phase distortion of the received signal. Non-coherent detection atthe receiver is preferred to coherent detection because of the relativesimplicity at the receiver.

[0006] As is well known from those skilled in the art, orthogonalmodulation are conventionally used since specially good appropriate fornon-coherent detection at the receiver. However, signals modulated by anorthogonal modulation are very bandwidth consuming. A compromise oftenconsists in reducing the bandwidth by using non-orthogonal modulationsresulting however in a performance degradation in the non-coherentdetector since the transmitted signals are correlated.

[0007] The design of multidimensional constellations for non-coherent,non-orthogonal modulations has proved to be a good way to compensate theperformance degradation at the non-coherent receiver.

[0008] In multiple users communication networks, there are several waysfor users to send information through the communication channel. Forboth Time Division Multiple Access (TDMA) and Frequency DivisionMultiple Access (FDMA) techniques, the channel is basically partitionedinto equal independent and non-overlapping single user subchannels. Eachuser is respectively assigned a particular time slot within each frameor a frequency subchannel. These techniques are frequently used in dataand digital voice transmission. However both methods tend to beinefficient when users transmit bursty information. In this particularcase, an alternative is to allow more than one user to share a channelor subchannel by use of direct-sequence spread spectrum signals. In thistechnique, called Code Division Multiple Access (CDMA), each user isassigned a unique code sequence and spreads the information signalacross the assigned frequency band. Thus, signals from the various usersare separated at the receiver by cross-correlation of the receivedsignal with each of the possible user signature sequences. CDMA is apromising technique for radio access in future cellular mobile andpersonal communication systems. It offers some attractive featurescompared to TDMA or FDMA such as the potential for high radio capacity,soft handover, simplified frequency planning, etc.

[0009] In non-coherent TDMA and FDMA systems, Q-ary Frequency ShiftKeying (FSK) is used and non-coherent detection is made with Qorthogonal FSK signals having a tone spacing equal to the inverse of thesymbol period. Reducing the tone spacing of FSK signals leads tonon-orthogonal modulations that can be advantageously used to reduce thebandwidth of the modulated signals.

[0010] In non-coherent CDMA systems, the modulation is preferably chosento be a family of orthogonal spreading sequences, e.g. Walsh-Hadamard.However, the number of strictly orthogonal spreading sequences islimited for a given spreading sequence length (the spectral efficiencyof orthogonal spreading sequences is poor). Non-orthogonal spreadingsequences are then advantageously used to enhance the system capacity.They are mainly characterised by their cross-correlation, which isequivalent to the tone non-orthogonality in the FSK case.

[0011] A known solution is to replace the Walsh-Hadamard set by a newnon-orthogonal set. When this kind of sets cannot be used, one can thinkof considering several masked versions of an initially orthogonal set(used for instance in IS-95 systems). An alternative is to use wellknown families of PN-like sequences (e.g. Gold or Kasami sequences).

[0012] U.S. Pat. No. 5,938,787 describes a method of encodinginformation symbols according to a concatenation of an error correctioncode and a non-orthogonal modulation code where the non-orthogonalmodulation code is obtained by a translation of a set of orthogonal codevectors according to a predetermined translation. This modulation setcontains spreading sequences with binary chip values. This fact impliesa strong limitation on the number of spreading sequences that could begenerated. Indeed, when considering spreading sequences of N chipslength, the ultimate upper limit on the number of spreading sequences is2^(N). A large number of these 2^(N) spreading sequences is not usablesince a limit for the cross-correlation value between the spreadingsequences should be ensured.

[0013] In “Complex spreading sequences with a wide range of correlationproperties” (I. Opperman and B. Vucetic, IEEE transaction oncommunications, VOL. 45 NO. 3, March 1997, pages 365 to 375), a methodfor building sets of complex spreading sequences with good correlationproperties is presented. For ensuring good correlation properties, thenumber of spreading sequences M constituting the alphabet is chosensmaller than the spreading sequence length N.

[0014] All above described modulation sets have a low spectralefficiency. The spectral efficiency can defined be as log₂(M)/N andrepresents the number of bits to map a sequence divided by the sequencelength. This quantity is given in bit/s/Hz. For the modulation setsdescribed above, the spectral efficiency is <<1 (very smaller than one).

[0015] The object of the present invention is to provide a method fortransmitting coded information symbols in a communication network byusing a non-orthogonal modulation code having a large spectralefficiency.

[0016] Another object of the invention is to provide a non-orthogonalmodulator for performing the above mentioned method.

[0017] Another object of the present invention is to providenon-orthogonal modulation codes families to be used by thenon-orthogonal modulator.

SUMMARY OF THE INVENTION

[0018] These objects, and others that appear below, are achieved by amethod for modulating information symbols to be transmitted in a CDMAcommunication network by using a non-orthogonal modulation codecomprising M spreading sequences (s_(m) 1≦m≦M), each comprising in Nchips (s_(m,n) 1<n≦N) used to modulate said coded information symbols,said M spreading sequences having the same energy$\left( {\sum\limits_{n = 1}^{N}s_{m,n}^{2}} \right),$

[0019] the amplitude of said chips taking a plurality of values, andsaid number M of spreading sequences being higher than the number ofchips N per spreading sequence.

[0020] These objects are also achieved by a non-orthogonal modulationcodes family comprising M spreading sequences (s_(m) 1≦m≦M), eachcomprising in N chips (s_(m,n) 1≦n≦N) used to modulate said codedinformation symbols, said M spreading sequences having the same energy$\left( {\sum\limits_{n = 1}^{N}s_{m,n}^{2}} \right),$

[0021] the amplitude of said chips taking a plurality of values; andsaid number M of spreading sequences being higher than the number ofchips N per spreading sequence.

[0022] These objects are further attained by a modulator for modulatingcoded information signal with non-orthogonal spreading sequencescharacterized in that it comprises:

[0023] means for generating non-orthogonal spreading sequence familiescomprising M spreading sequences (s_(m) 1≦m≦M), each comprising in Nchips (s_(m,n) 1≦n≦N) used to modulate said coded information symbols,said M spreading sequences having the same energy$\left( {\sum\limits_{n = 1}^{N}s_{m,n}^{2}} \right),$

[0024]  the amplitude of said chips taking a plurality of values;

[0025] and said number M of spreading sequences being higher than thenumber of chips N per spreading sequence; and

[0026] means for storing said non-orthogonal spreading sequences.

[0027] The spreading sequence sets according to the invention have theadvantage to have a spectral efficiency that can easily exceed 1bit/s/Hz.

[0028] Another advantage of this method is that it increases thecapacity of the communication network.

[0029] In a preferred embodiment of the invention, the spreadingsequences constituting the non-orthogonal modulation code have a crosscorrelation smaller than a predefined threshold.

[0030] In another preferred embodiment, the modulation code according tothe invention is combined with an efficient error correction code tocompensate the fact that the correlation between the spreading sequencesof the sets are not negligible.

[0031] Further advantageous features of the invention are defined in thedependent claims.

[0032] This invention is based on a priority application EP 00 44 0287which is hereby incorporated by reference.

BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Other characteristics and advantages of the invention will appearon reading the following description of a preferred implementation givenby way of non-limiting illustrations, and from the accompanyingdrawings, in which:

[0034]FIG. 1 shows a communication chain where a non-orthogonalmodulation code according to the invention can be used;

[0035]FIG. 2 shows a set of non-orthogonal spreading sequences accordingto the invention having a sequence length of 2. FIG. 2a is a geometricalrepresentation of these, FIG. 2b represents the corresponding modulationcodes and FIG. 2c represents an example of information flow modulatedwith said spreading sequences;

[0036]FIG. 3 shows the performance of a non-orthogonal spreadingsequence set according to the invention compared to an orthogonalsequence set for a Additive White Gaussian Noise (AWGN) channel;

[0037]FIG. 4 shows the performance of a non-orthogonal spreadingsequence set according to the invention compared to an orthogonalsequence set for a Raleigh fading channel.

DETAILED DESCRIPTION OF THE INVENTION

[0038]FIG. 1 shows a communication chain where a non-orthogonalmodulation code according to the invention can be used. Communicationchain comprises a transmit part 11, a radio channel 12 and a receiverpart 13. Transmit part comprises an information source 111, an encoder112, an interleaver 113, a non-orthogonal modulator 114. Receiver partcomprises a non-coherent demodulator 131, a deinterleaver 132 and adecoder 133. Non-orthogonal modulator 114, as known in the art, isresponsible for transforming a numeric information flow composed ofsequence of digital symbols in an electrical signal. Non-orthogonalmodulator 114 supports the method according to the invention andgenerates an electrical signal having a period equal to the chipduration and an amplitude depending on the used spreading sequences.Spreading sequences to be used are generated and stored atnon-orthogonal modulator 114.

[0039] A unique spreading sequence may be used at non-orthogonalmodulator 114 as in usual multiple user CDMA systems. In that case, eachuser is allocated one spreading sequence. The information flowtransmitted by each user is spread by the spreading sequence (i.e eachsymbol to be modulated is multiplied by the spreading sequence). In theuplink, the receiver (i.e. a base station) receives a composed signalconsisting in a superposition of spread signals spread with differentspreading sequences. By correlating the composed signal with thedifferent spreading sequences, the receiver can extract the informationflow of each user from the composed signal.

[0040] Alternatively, several spreading sequences may be used at thenon-orthogonal modulator 114. In that case, the incoming digitalinformation flow at the non-orthogonal modulator is considered as groupsof K bits. There are 2^(K) possible groups of K bits. One spreadingsequence is associated to each group of K bits. The modulator uses 2^(K)spreading sequences to modulate the signal. One spreading sequencecorresponds in that case to one modulation symbol. This technique iscalled coded modulation. The electrical signal generated bynon-orthogonal modulator 114 is a succession of electrical signalsrepresenting the successive spreading sequences associated to thesuccessive symbols to transmit.

[0041] Any combination of the two above mentioned applications may beenvisaged. For all these applications, the design of appropriatenon-orthogonal spreading sequences is essential.

[0042] According to the invention, the proposed construction methodconsists in designing non-orthogonal spreading sequence sets containinga large number of spreading sequences M (M>>sequence length N) andensuring a reasonable correlation value by allowing the chip value to beany real number instead of only ±1 as known in the art. These spreadingsequences should be chosen with equal energy.

[0043] Geometrically this is equivalent to place M points on anN-dimensional sphere, while ensuring a good repartition of thecorrelations.

[0044] Each one of the M spreading sequences is related to one of Mpoints on the N-dimensional sphere. The N components (chips) s_(m,n)1≦n≦N of a spreading sequence are coordinates of the associated point onthe N-dimensional sphere. The cross-correlation values between spreadingsequences are directly related to angles between the associated points.The energy of the spreading sequence is proportional to$\sum\limits_{n = 1}^{N}s_{m,n}^{2}$

[0045] When allowing the use of the whole sphere, we can finddiametrically opposed points, leading to a correlation value equal to 1.In that case, it would be impossible to distinguish at demodulationbetween the two spreading sequences.

[0046] Preferably, the M points should be placed on a half of theN-dimensional sphere only, so that the maximal correlation value neverreaches one and remains smaller than a predefined threshold valuesmaller than one. A possible threshold values is 0,5. Other thresholdvalues may be envisaged depending on the maximum acceptedcross-correlation.

[0047] Real as well as complex spreading sequences are considered in thepresent invention. Complex spreading sequences being essentially usedfor base band transmission with an in-phase and in-quadrature path.

[0048] In the following several examples are given to illustrate sets ofspreading sequences according to the present invention.

[0049]FIG. 2 shows an example of a non-orthogonal spreading sequence setaccording to the invention having a sequence length of 2.

[0050] The case M=8, N=2 corresponds to a family of 8 spreadingsequences (s₁, . . . , s₈) of length 2 detailed below.

[0051] s₁ (1,0)   s₂ (0.923, 0.382)

[0052] s₃ (0.707, 0.707)   s₄ (0.382, 0.923)

[0053] s₅ (0, 1)   s₆ (−0.382, 0.923)

[0054] s₇ (−0.707, 0.707)   s₈ (−0.923, 0.382)

[0055]FIG. 2a gives the geometrical representation when the choice ofthe 8 points corresponding to the 8 spreading sequences of length 2 arelocated on the half unitary circle. The corresponding eight modulationcode signals of length 2 are represented on FIG. 2b. In this case thechip value are chosen among a set of 8 chip values: 1, 0, 0,923, 0.382,0.707, −0.382, −0.707, −0.923.

[0056]FIG. 2c represents an example of code modulated signal. In thatcase the digital sequence 000100101110111001010111 is modulatedaccording to the present invention. One user is allocated all eightspreading sequences (s₁, . . . , s₈). The bits of the digital sequencesare grouped by three and each of the eight possible value for a group ofthree bits is attributed one of the eight spreading sequences.

[0057] Assumed that s₁ represents 000, s₂ represents 001, s₃ represents010, . . . , s₈ represents 111, then the modulated signal for thedigital sequence is represented by the succession of spreading sequencess₁, s₅, s₆, s₇, s₈, s₂, s₃, s₈.

[0058] The correlation between any two spreading sequences s_(i) ands_(j), defined as the inner product between both associated points, isgiven by μ_(i,j)=cos(α_(i,j)) where α_(i,j) is the angle between thegeometrical representations of s₁ and s_(j). μ_(i,j) is real and themaximum correlation value is given by μ_(max)=cos(π/8). If the thresholdvalue is set to μ_(max)=cos(π/8), the family of 8 spreading sequencefulfill the requirements regarding the maximum correlation between twospreading sequences of the set.

[0059] This can be generalized to the case of M spreading sequences oflength N=2 on the half unitary circle. For any couple (s_(i), s_(j)),with i≠j, μ_(max)=cos(π/M).

[0060] M is directly related to the spectral efficiency. A trade-off isnecessary between the spectral efficiency log₂(M)/N and the acceptableperformance degradation due to not negligible maximum correlation valuewhen M grows. The use of an efficient error correcting code incombination with a non-orthogonal modulation code according to theinvention enables it to minimize the disadvantage of high correlatingspreading sequences while increasing the capacity of the communicationnetwork.

[0061] A second example of a set of spreading sequences according to thepresent invention consists in considering lattice in higher dimensionspaces to build sets of spreading sequences having a higher length.

[0062] The Gosset lattice, E₈, is the densest lattice in dimension 8.The lattice points are assimilated to the centers of unit spheres onetangent to the other. The number of tangent spheres to one sphere in theGosset Lattice equals 240. Therefore, each point P of the lattice has240 neighbors at the same minimal distance. These 240 points are as aconsequence located on a sphere having as center the point P.

[0063] As a consequence, 240 spreading sequences having as eightsuccessive chip values the eight coordinates of one of the 240 pointsform a family of spreading sequences according to the present invention.

[0064] Thanks to geometrical considerations in the space of dimension 8,the minimum angle between any two points associated to a spreadingsequence is π/3, i.e. a maximal correlation cos(π/3)=0.5. As aconsequence if the threshold value is chosen equal to 0.5, thenon-orthogonal spreading sequence code comprises 240 spreadingsequences.

[0065] This leads to the design of a family of 240 spreading sequencesof length eight having a maximum correlation of 0.5 in comparison to theeight orthogonal sequences of length eight given by the Walsh-Hadamardset having a maximal correlation of zero.

[0066] The previous example can be generalized as follows:

[0067] Let's denote Ω_(N) the unit sphere of R^(N) and (*) the usualinner product and (N,M,s) a subset of Ω_(N) of size M for which (u*v)≧sfor all u,v ε subset and u≠v.

[0068] In the previous example, the subset (8,240,0.5) of Ω₈ has beenconsidered.

[0069] In dimension 24, the subset (24, 196560, 0.5) can be extractedfrom the Leech lattice Λ₂₄, and is also a modulation code according tothe construction method of the present invention.

[0070] For a given length N, a subset according to the present inventionextracted from a dense integer lattice always gives the maximum numberof non-orthogonal spreading sequences with a correlation between eachcouple of spreading sequences smaller than a predefined threshold, thanif the code were extracted from another lattice.

[0071] Another example of set of spreading sequences according to thepresent invention can be constructed as follows.

[0072] In analogy to a M-PSK (Pulse Shift Keying) modulation, a set ofcomplex spreading sequence according to the present invention can beobtained.

[0073] A M-PSK modulating signal u_(m)(t) can be expressed as follows:${u_{m}(t)} = {{\exp \left( {j\phi}_{m} \right)} = {\exp \left( {j\quad \frac{\quad {2\quad \pi}}{M}\left( {m - 1} \right)t} \right)}}$for  m = 1, …  , M  and  ϕ_(m) ∈ [0, 2π].

[0074] Each component (chip) s_(m,n) 1≦m≦M of the nth. complex spreadingsequence of the set is associated to one of the M possible phases in theM-PSK:$s_{m,n} = {{\frac{1}{\sqrt{N}}{\exp \left( {j\quad \frac{2\pi}{M} \times {\left( {\left( {n - 1} \right)\left( {m - 1} \right)} \right)\lbrack M\rbrack}} \right)}} = {\frac{1}{\sqrt{N}}{\exp \left( {j\quad \beta_{m,n}} \right)}}}$

[0075] where n[M] denotes n modulo M. The phase β_(m,n) is in [0,2π]when n=1, . . . , N and m=1, . . . , M.

[0076] The obtained M spreading sequences are distributed on anN-dimensional unit sphere.

[0077] Another example of a set of complex spreading sequences accordingto the present invention, consists in selecting M randomly chosencomplex spreading sequences s_(m) 1≦m≦M of length N on a N-dimensionalunit complex sphere.$s_{m} = {\frac{1}{\sqrt{N}}\left( {^{{j\phi}_{1}},^{j\quad \phi_{2}},\ldots \quad,^{{j\phi}_{N}}} \right)}$

[0078] where Φ_(n) is a random variable uniformly distributed on [0,2π].

[0079] FIGS. 3, respectively FIG. 4, illustrates the performance ofrandomly generated non-orthogonal sets of complex spreading sequencesfor a AWGN channel, respectively for a Rayleigh fading channel.

[0080] For non-orthogonal signals and for a given size M of the set ofspreading sequences, the envelope of the maximum achievable capacitycurves with respect to Eb/N₀ for various lengths N is represented on thediagrams shown of FIGS. 3 and 4.

[0081] As reference to compare the performance, the envelope of capacitycurves is also given for various N for orthogonal spreading sequences(M=N in this case).

[0082] Moreover, for comparison, we include a curve of the capacity ofthe considered AWGN or Rayleigh fading channel with coherent detectionwhich represents an absolute upper limit.

[0083] Preferably, the non-coherent receiver for correlated signalsconsists in a maximum envelope detector at the output of the matchedfilters.

[0084] For all curves, the capacity is given in bit/s/Hz i.e. bits percomplex dimension.

[0085] Non-orthogonal set of spreading sequences largely outperformorthogonal ones from a mutual information point of view whicheverchannel is considered. This performance enhancement can be obtained inpractice with a reduced increase of the complexity.

[0086] For instance, a family of M=1024 correlated signals of length N=8reaches a mutual information of 1 bit/s/Hz with a loss of 3 dB whencompared to the coherent AWGN channel capacity (FIG. 3) while it reaches0.5 bit/s/Hz with a loss of 3.5 dB when compared to the coherentRayleigh channel capacity (FIG. 4).

[0087] For both channels, there is no orthogonal spreading sequence setable to exceed a mutual information of 0.5 bit/s/Hz. This maximum isreached by both orthogonal sets of size N=2 and N=4 at Eb/N₀ values farfrom the ones of the coherent channel capacity curves (respectively 8and 16 dB on AWGN and Rayleigh channels).

[0088] However, with non-orthogonal signals, an increase of either theset size M or the sequence length N always leads to higher spectralefficiencies. Hence, there is a trade-off between the improvement ofspectrum efficiency and the complexity of the set of spreadingsequences.

[0089] According to the diagram shown on both FIG. 3 and FIG. 4, thenon-orthogonal spreading sequence sets according to the presentinvention exhibit higher spectral efficiency than orthogonal sets andincrease the capacity of the communication network.

[0090] The increase of the capacity of the communication network ispreferably obtained by combining an efficient error correcting code tothe use of the non-orthogonal spreading sequences according to thepresent invention. For example, a convolutional ⅔ encoding (octalgenerators 27, 75, 72) of a set of M=64 spreading sequences of lengthN=8 leads to a loss of only 2 dB from the maximum achievable capacity onAWGN non-coherent channel.

[0091] The method according to the invention may as well be used in asystem combining CDMA (Code Division Multiple Access) and TDMA (TimeDivision Multiple Access) techniques also called TD-CDMA.

1. Method for modulating information symbols to be transmitted in a CDMAcommunication network by using a non-orthogonal modulation codecomprising m spreading sequences (s_(m) 1≦m≦M), each comprising in Nchips (s_(m,n) 1≦n≦n) used to modulate said coded information symbols,said m spreading sequences having the same energy$\left( {\sum\limits_{n = 1}^{N}s_{m,n}^{2}} \right),$

the amplitude of said chips taking a plurality of values, and saidnumber m of spreading sequences being higher than the number of chips nper spreading sequence.
 2. Method according to claim 1, characterized inthat the correlation between each couple of said spreading sequences issmaller than a predefined threshold.
 3. Method according to any of theclaims 1 to 2, characterized in that said spreading sequences areextracted from a dense lattice in a space of dimension N.
 4. Methodaccording to claim 3, characterized in that said spreading sequences areextracted from the Gosset lattice (N=8).
 5. Method according to claim 3,characterized in that said spreading sequences are extracted from theLeech lattice (N=24).
 6. Method according to any of the claims 1 or 2,characterized in that said chip values correspond to the coordinates ofpoints randomly chosen on an N-dimensional complex sphere.
 7. Methodaccording to any of the claims 1 to 6, characterized in that saidsymbols are coded with an efficient error correction code. 8.Non-orthogonal modulation code families comprising M spreading sequences(s_(m) 1≦m≦M), each comprising in N chips (s_(m,n) 1≦n≦N) used tomodulate said coded information symbols, said M spreading sequenceshaving the same energy$\left( {\sum\limits_{n = 1}^{N}s_{m,n}^{2}} \right),$

the amplitude of said chips taking a plurality of values; and saidnumber M of spreading sequences being higher than the number of chips Nper spreading sequence.
 9. Modulator for modulating coded informationsignal with non-orthogonal spreading sequences characterized in that itcomprises means for generating non-orthogonal spreading sequencefamilies according to claim 7; and means for storing said non-orthogonalspreading sequences.